Properties

Label 2450.j
Number of curves $2$
Conductor $2450$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2450.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.j1 2450o2 \([1, -1, 0, -6827, -215419]\) \(-5745702166029/8192\) \(-50176000\) \([]\) \(1872\) \(0.74903\)  
2450.j2 2450o1 \([1, -1, 0, -2, 6]\) \(-189/2\) \(-12250\) \([]\) \(144\) \(-0.53344\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2450.j have rank \(1\).

Complex multiplication

The elliptic curves in class 2450.j do not have complex multiplication.

Modular form 2450.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 3 q^{9} + 3 q^{11} - 5 q^{13} + q^{16} - 2 q^{17} + 3 q^{18} + 5 q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.